Understanding the Origin of the Particularly Small and Anisotropic Thermal Expansion of MOF‐74

Metal–organic frameworks often display large positive or negative thermal expansion coefficients. MOF-74, a material envisioned for many applications, shows a different behavior. Temperature-dependent X-ray diffraction reveals particularly small negative (positive) thermal expansion coefficients perpendicular (parallel) to the hexagonally arranged pores. These trends are explained by combining density-functional theory calculations with the Grüneisen theory of thermal expansion, which allows tracing back thermal expansion to contributions of individual phonons. On the macroscopic level, the small thermal expansion coefficients arise from compensation effects caused by the large coupling between perpendicular stress and strain and by the small magnitudes of the mean Grüneisen tensor elements, 〈γ〉. These provide information on how strains impact phonon frequencies. To understand the small value of 〈 (Formula presented.) 〉, the individual mode contributions are analyzed using the corresponding atomic motions. This reveals that only the lowest frequency modes up to ≈3 THz provide non-negligible contributions, such that 〈 (Formula presented.) 〉 drops sharply at higher temperatures. These considerations reveal, how the details of the anharmonic properties of specific phonon bands determine the magnitude and sign of thermal expansion in a prototypical material like MOF-74. Beyond that, the authors also discuss, how the choice of the theoretical methodology impacts the obtained results.